"To take a leap" and "to make a leap" are interchangeable.
However the expression doesn't come from imagery of leaping over an obstacle like an object. Instead, it is more like leaping between two points with a bottomless chasm between them, like so.
Taking a leap of faith is a very common expression, implying that the individual must have faith (either in themselves, or somebody else, or god) that they will survive the leap.
"Taking the plunge," has a different meaning. It comes from experience of going to a a pool and jumping right into it and getting all wet at once, instead of getting in the pool little by little to get yourself accustomed to the water.
The two have subtly different meanings. If you take the leap, you're jumping across and into something new. Whereas if you take the plunge, you fully immersing yourself into something instead of taking baby steps to get there.